A) \[P({{E}^{c}})+P({{F}^{c}})\]
B) \[P({{E}^{c}})-P({{F}^{c}})\]
C) \[P({{E}^{c}})-P(F)\]
D) \[P(E)-P({{F}^{c}})\]
Correct Answer: C
Solution :
[c] We have \[\therefore E\cap F\cap G=\phi \] \[P({{E}^{c}}\cap {{F}^{c}}/G)=\frac{P({{E}^{c}}\cap {{F}^{c}}\cap G)}{P(G)}\] \[=\frac{P(G)-P(E\cap G)-P(G\cap F)}{P(G)}\] [From Venn diagram \[{{E}^{c}}\cap {{F}^{c}}\cap G=G-E\cap G-F\cap G\]] \[=\frac{P(G)-P(E)P(G)-P(G)p(F)}{P(G)}\] \[=1-P(E)-P(F)=P({{E}^{c}})-P(F)\] [\[\therefore \] E, F, G are pairwise independent]You need to login to perform this action.
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